1. Field of the Invention
The present invention relates generally to a method of compensating the output of an exhaust gas sensor or air/fuel ratio sensor, and more particularly to a method of compensating the output of such an air/fuel ratio sensor, for improved accuracy of measurement or determination, or regulation or control of the air/fuel ratio of an air-fuel mixture supplied to an internal combustion engine of a motor vehicle or an industrial furnace.
2. Discussion of the Prior Art
In the art of measuring the air/fuel ratio (A/F ratio) or other parameter of an air/fuel mixture used for an automotive internal combustion engine or an industrial furnace, there is known an exhaust gas sensor or air/fuel ratio sensor of a so-called double-cell type which uses in combination an electrochemical cell in the form of an oxygen concentration cell, and another electrochemical cell in the form of an oxygen pumping cell. In use, the air/fuel ratio sensor is exposed to an exhaust gas produced as a result of combustion of the air-fuel mixture. Since the level of output signal of the air/fuel ratio sensor has known relationships with the contents of the individual components of the exhaust gas, a parameter or parameters of the air-fuel mixture such as the air/fuel ratio (A/F), excess oxygen ratio (.lambda.) and oxygen concentration (+O.sub.2 or -O.sub.2) can be determined based on the output signal of the sensor.
Each of the two electrochemical cells of the double-cell type air/fuel ratio sensor uses an oxygen-ion conductive solid electrolyte body, and at least one pair of electrodes provided on the solid electrolyte body. Between the two electrochemical cells, there is formed an internal space into which the exhaust gas under measurement is introduced under a predetermined diffusion resistance. The first or oxygen concentration sensing cell (hereinafter referred to as "sensing cell") produces an electromotive force depending upon the partial pressure of oxygen in the internal space, according to the Nernst equation, while the second or oxygen pumping cell (hereinafter referred to as "pumping cell") operates to perform an oxygen pumping action so as to regulate the oxygen partial pressure within the internal space of the sensor so that the electromotive force induced by the sensing cell is held at a predetermined constant level which corresponds to the stoichiometric point (A/F=14.6; .lambda.=1). The pump current applied to the pumping cell is used as the output of the air/fuel ratio sensor, which reflects the composition of the exhaust gas.
More specifically described, the pump current Ip applied to the pumping cell in this double-cell type of air/fuel ratio sensor is obtained according to the following equation (1): EQU Ip=KO.sub.2 .multidot.PO.sub.2 -KCO.multidot.PCO-KH.sub.2 .multidot.PH.sub.2 ( 1)
where,
KO.sub.2 : O.sub.2 concentration current sensitivity coefficient PA1 PO.sub.2 : Partial pressure of O.sub.2 in exhaust gas PA1 KCO: CO concentration current sensitivity coefficient PA1 PCO: Partial pressure of CO in exhaust gas PA1 KH.sub.2 : H.sub.2 concentration current sensitivity coefficient PA1 PH.sub.2 : Partial pressure of H.sub.2 in exhaust gas PA1 CmHn: Carbon-hydrogen fuel PA1 m: Number of carbon component in 1 mole of the fuel PA1 n: Number of hydrogen component in 1 mole of the fuel PA1 .lambda.: Excess air ratio PA1 A.sub.1 -A.sub.6 : Numbers of the appropriate components in exhaust gas PA1 PCO: Partial pressure of CO in exhaust gas PA1 PH.sub.2 O: Partial pressure of H.sub.2 O in exhaust gas PA1 PCO.sub.2 : Partial pressure of PCO.sub.2 in exhaust gas PA1 PH.sub.2 : Partial pressure of H.sub.2 in exhaust gas
The output of the sensor in the form of the pump current Ip is then processed to calculate the A/F ratio, etc., according to the following formulas (2A) and (2B) and equation (3). The formulas (2A) and (2B) are associated with the numbers of the individual components of the air-fuel mixture before combustion and those of the exhaust gas produced as a result of combustion of the air-fuel mixture.
i) Air-Fuel Mixture Before Combustion: EQU CmHn+.lambda..multidot.{O.sub.2 +(m+n/4).multidot.(79.05/20.95).multidot.N.sub.2 } (2A)
ii) Exhaust Gas Produced by Combustion of Air-Fuel Mixture: EQU A.sub.1 .multidot.CO+A.sub.2 .multidot.CO.sub.2 +A.sub.3 .multidot.H.sub.2 +A.sub.4 .multidot.H.sub.2 O+A.sub.5 .multidot.O.sub.2 +A.sub.6 .multidot.N.sub.2 ( 2B)
where,
Generally, A.sub.1 .multidot.CO and A.sub.3 .multidot.H.sub.2 are approximately 0% where .lambda..gtoreq.1, and are not 0% where .lambda.&lt;1. EQU K(t)=(PCO.multidot.PH.sub.2)/(PCO.sub.2 .multidot.PH.sub.2) (3)
where,
The current sensitivity coefficients KO.sub.2, KCO and KH.sub.2 in the equation (1) are coefficients of sensitivity of the pump current Ip to the concentrations of the gas components O.sub.2, CO and H.sub.2 of the exhaust gas. These coefficients KO.sub.2, KCO and KH.sub.2 are constants which are determined and influenced by specific characteristics of the individual sensors, such as the diffusion resistance under which the exhaust gas is introduced into the internal space of the sensor. In other words, the actual current sensitivity coefficients of one sensor differ from those of another sensor, since the individual sensors more or less have dimensional or other manufacturing errors or deviations from the nominal values.
Therefore, the outputs of the individual sensors should be compensated for the variations in the actual current sensitivity coefficients of the gas components of the exhaust gas, by actually measuring those current sensitivity coefficients when the sensors are exposed to a calibrating gas. Otherwise, the output of one sensor may differ from that of another sensor, even when the exhaust gases to be measured by these sensors have the same composition. Thus, the individual sensors should be calibrated for compensation of their outputs for the difference in the actual current sensitivity coefficients of the individual sensors.
Laid-open Publication No. 62-257056 (published in 1987) of unexamined Japanese Patent Application discloses an example of recently proposed methods for easy and precise compensation of the outputs of the individual sensors for the difference in the actual coefficients of sensitivity of the pump current to the gas components of the exhaust gas. In the method disclosed therein, the analog output signal of the sensor is first converted into a digital signal by an A/D converter, and the digital signal is processed for compensating the sensor output according to the actual current sensitivity coefficients of the sensor.
In the presence of the difference or variation in the actual current sensitivity coefficients of the individual sensors, the range over which the output level of a given sensor changes in operation may considerably differ from that of another sensor. In the above-indicated method, therefore, the range of change in the output level of a sensor may be extremely narrower than the nominal range FSR of the input signal of the A/D converter, which is defined by the maximum and minimum levels of the input analog signal, which is the output of the sensor, usually in the form of a voltage signal. In this case, a quantizing error which occurs upon conversion of the analog signal into a digital signal by the A/D converter will have a considerably large influence on the digital output of the A/D converter, whereby the sensing accuracy of the sensor is deteriorated.
For example, if the maximum pump current (Ipmax) obtained with respect to a given calibrating gas is 10 mA for one sensor, and 2 mA for another sensor, due to different current sensitivity coefficients of the two sensors, the maximum level of the analog voltage signal applied to the A/D converter for the former sensor is five times as high as that of the analog voltage signal applied to the A/D converter for the latter sensor. In this case, the amount of error included in the obtained digital output signal of the A/D converter for the latter sensor due to the quantizing error is five times as large as that for the former sensor.
No solutions have been heretofore proposed to effectively deal with the deterioration of the sensing accuracy of the known air/fuel ratio sensors due to the quantizing error described above. The only method to avoid this accuracy deterioration has been to measure or detect the actual output characteristics of the individual sensors and use only the sensors whose output characteristics meet the predetermined standards.
An A/D converter has generally an electrical tendency that the quantizing error becomes excessively large when the level of the analog input signal is less than 1/5 of the nominal input signal range FSR of the converter. Where the sensor is used as an air/fuel ratio sensor exposed to an exhaust gas of an automotive engine, the sensing accuracy tends to be comparatively low because the level of the input analog signal of the A/D converter is relatively low, since the air/fuel ratio of an air-fuel mixture which produces the exhaust gas is controlled to be close to the stoichiometric point (14.6), which means that the input level of the A/D converter and the output level of the air/fuel ratio sensor are usually zero or close to zero. Consequently, the sensor suffers from low sensing accuracy due to a large influence of the quantizing error of the A/D converter.